Finite Group Databasebeta

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C23×C4×C5×C8×C11 #72192245

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3523215360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C4×C5×C8×C11
multiplicative(ℤ/37720)ˣ, (ℤ/39160)ˣ, (ℤ/40480)ˣ, (ℤ/45264)ˣ, (ℤ/46992)ˣ, (ℤ/53400)ˣ, (ℤ/55200)ˣ, (ℤ/56580)ˣ, (ℤ/58080)ˣ, (ℤ/58740)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C25×C5×C11
socle, prime radicalC25×C5×C11C2×C4
LCSG ▷ C1
UCSC1 ◁ G

9276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C11×C16, C23×C5×C82×C11, C22×C42×C5×C8×C11, …
maximal normal subgroup ofC23×C4×C5×C11×C16, C23×C5×C82×C11, C22×C42×C5×C8×C11, …
maximal quotient ofC23×C4×C5×C11×C16, C23×C5×C82×C11, C22×C42×C5×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.